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A307401 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} k*x^k*A(x)^k/(1 + x^k*A(x)^k). 2
1, 1, 2, 8, 26, 92, 360, 1416, 5698, 23513, 98346, 416418, 1783144, 7704322, 33546344, 147071592, 648636050, 2875822121, 12810531924, 57306505152, 257330920910, 1159517118330, 5241137123470, 23758569938458, 107983949179512, 491985193384077, 2246564114646650 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

FORMULA

G.f. A(x) satisfies: A(x) = (23 + theta_2(x*A(x))^4 + theta_3(x*A(x))^4)/24.

G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} A000593(k)*x^k*A(x)^k.

G.f.: A(x) = (1/x)*Series_Reversion(x/(1 + Sum_{k>=1} A000593(k)*x^k)).

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 26*x^4 + 92*x^5 + 360*x^6 + 1416*x^7 + 5698*x^8 + 23513*x^9 + 98346*x^10 + ...

MATHEMATICA

terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[k x^k A[x]^k/(1 + x^k A[x]^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[Sum[(-1)^(k/d + 1) d, {d, Divisors[k]}] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

terms = 27; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[Sum[(-1)^(k/d + 1) d, {d, Divisors[k]}] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]

CROSSREFS

Cf. A000593, A190790, A192206, A307397, A307399.

Sequence in context: A320802 A052543 A026638 * A067855 A301699 A129368

Adjacent sequences:  A307398 A307399 A307400 * A307402 A307403 A307404

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 07 2019

STATUS

approved

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Last modified May 15 06:46 EDT 2021. Contains 343909 sequences. (Running on oeis4.)